mlogit: Multinomial logit model
In mlogit: Multinomial Logit Models
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
Estimation by maximum likelihood of the multinomial logit model,
with alternative-specific and/or individual specific variables.
Usage
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mlogit(
formula,
data,
subset,
weights,
na.action,
start = NULL,
alt.subset = NULL,
reflevel = NULL,
nests = NULL,
un.nest.el = FALSE,
unscaled = FALSE,
heterosc = FALSE,
rpar = NULL,
probit = FALSE,
R = 40,
correlation = FALSE,
halton = NULL,
random.nb = NULL,
panel = FALSE,
estimate = TRUE,
seed = 10,
...
)
Arguments
formula
a symbolic description of the model to be estimated,
data
the data: an mlogit.data object or an ordinary
data.frame,
subset
an optional vector specifying a subset of
observations for mlogit,
weights
an optional vector of weights,
na.action
a function which indicates what should happen when
the data contains NAs,
start
a vector of starting values,
alt.subset
a vector of character strings containing the
subset of alternative on which the model should be estimated,
reflevel
the base alternative (the one for which the
coefficients of individual-specific variables are normalized to
0),
nests
a named list of characters vectors, each names being a
nest, the corresponding vector being the set of alternatives
that belong to this nest,
un.nest.el
a boolean, if TRUE, the hypothesis of unique
elasticity is imposed for nested logit models,
unscaled
a boolean, if TRUE, the unscaled version of the
nested logit model is estimated,
heterosc
a boolean, if TRUE, the heteroscedastic logit
model is estimated,
rpar
a named vector whose names are the random parameters
and values the distribution : 'n' for normal, 'l' for
log-normal, 't' for truncated normal, 'u' for uniform,
probit
if TRUE, a multinomial porbit model is estimated,
R
the number of function evaluation for the gaussian
quadrature method used if heterosc = TRUE, the number of
draws of pseudo-random numbers if rpar is not NULL,
correlation
only relevant if rpar is not NULL, if true,
the correlation between random parameters is taken into
account,
halton
only relevant if rpar is not NULL, if not NULL,
halton sequence is used instead of pseudo-random numbers. If
halton = NA, some default values are used for the prime of
the sequence (actually, the primes are used in order) and for
the number of elements droped. Otherwise, halton should be a
list with elements prime (the primes used) and drop (the
number of elements droped).
random.nb
only relevant if rpar is not NULL, a
user-supplied matrix of random,
panel
only relevant if rpar is not NULL and if the data
are repeated observations of the same unit ; if TRUE, the
mixed-logit model is estimated using panel techniques,
estimate
a boolean indicating whether the model should be
estimated or not: if not, the model.frame is returned,
seed
the seed to use for random numbers (for mixed logit and
probit models),
...
further arguments passed to mlogit.data or
mlogit.optim.
Details
For how to use the formula argument, see Formula().
The data argument may be an ordinary data.frame. In this case,
some supplementary arguments should be provided and are passed to
mlogit.data(). Note that it is not necessary to indicate the
choice argument as it is deduced from the formula.
The model is estimated using the mlogit.optim().
function.
The basic multinomial logit model and three important extentions of
this model may be estimated.
If heterosc=TRUE, the heteroscedastic logit model is estimated.
J - 1 extra coefficients are estimated that represent the scale
parameter for J - 1 alternatives, the scale parameter for the
reference alternative being normalized to 1. The probabilities
don't have a closed form, they are estimated using a gaussian
quadrature method.
If nests is not NULL, the nested logit model is estimated.
If rpar is not NULL, the random parameter model is estimated.
The probabilities are approximated using simulations with R draws
and halton sequences are used if halton is not
NULL. Pseudo-random numbers are drawns from a standard normal and
the relevant transformations are performed to obtain numbers drawns
from a normal, log-normal, censored-normal or uniform
distribution. If correlation = TRUE, the correlation between the
random parameters are taken into account by estimating the
components of the cholesky decomposition of the covariance
matrix. With G random parameters, without correlation G standard
deviations are estimated, with correlation G * (G + 1) /2
coefficients are estimated.
Value
An object of class "mlogit", a list with elements:
coefficients: the named vector of coefficients,
logLik: the value of the log-likelihood,
hessian: the hessian of the log-likelihood at convergence,
gradient: the gradient of the log-likelihood at convergence,
call: the matched call,
est.stat: some information about the estimation (time used,
optimisation method),
freq: the frequency of choice,
residuals: the residuals,
fitted.values: the fitted values,
formula: the formula (a Formula object),
expanded.formula: the formula (a formula object),
model: the model frame used,
index: the index of the choice and of the alternatives.
Author(s)
Yves Croissant
References
\insertRefMCFA:73mlogit
\insertRefMCFA:74mlogit
\insertRefTRAI:09mlogit
See Also
mlogit.data() to shape the data. nnet::multinom() from
package nnet performs the estimation of the multinomial logit
model with individual specific variables. mlogit.optim()
details about the optimization function.
Examples
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## Cameron and Trivedi's Microeconometrics p.493 There are two
## alternative specific variables : price and catch one individual
## specific variable (income) and four fishing mode : beach, pier, boat,
## charter
data("Fishing", package = "mlogit")
Fish <- dfidx(Fishing, varying = 2:9, shape = "wide", choice = "mode")
## a pure "conditional" model
summary(mlogit(mode ~ price + catch, data = Fish))
## a pure "multinomial model"
summary(mlogit(mode ~ 0 | income, data = Fish))
## which can also be estimated using multinom (package nnet)
summary(nnet::multinom(mode ~ income, data = Fishing))
## a "mixed" model
m <- mlogit(mode ~ price + catch | income, data = Fish)
summary(m)
## same model with charter as the reference level
m <- mlogit(mode ~ price + catch | income, data = Fish, reflevel = "charter")
## same model with a subset of alternatives : charter, pier, beach
m <- mlogit(mode ~ price + catch | income, data = Fish,
alt.subset = c("charter", "pier", "beach"))
## model on unbalanced data i.e. for some observations, some
## alternatives are missing
# a data.frame in wide format with two missing prices
Fishing2 <- Fishing
Fishing2[1, "price.pier"] <- Fishing2[3, "price.beach"] <- NA
mlogit(mode ~ price + catch | income, Fishing2, shape = "wide", varying = 2:9)
# a data.frame in long format with three missing lines
data("TravelMode", package = "AER")
Tr2 <- TravelMode[-c(2, 7, 9),]
mlogit(choice ~ wait + gcost | income + size, Tr2)
## An heteroscedastic logit model
data("TravelMode", package = "AER")
hl <- mlogit(choice ~ wait + travel + vcost, TravelMode, heterosc = TRUE)
## A nested logit model
TravelMode$avincome <- with(TravelMode, income * (mode == "air"))
TravelMode$time <- with(TravelMode, travel + wait)/60
TravelMode$timeair <- with(TravelMode, time * I(mode == "air"))
TravelMode$income <- with(TravelMode, income / 10)
# Hensher and Greene (2002), table 1 p.8-9 model 5
TravelMode$incomeother <- with(TravelMode, ifelse(mode %in% c('air', 'car'), income, 0))
nl <- mlogit(choice ~ gcost + wait + incomeother, TravelMode,
nests = list(public = c('train', 'bus'), other = c('car','air')))
# same with a comon nest elasticity (model 1)
nl2 <- update(nl, un.nest.el = TRUE)
## a probit model
## Not run:
pr <- mlogit(choice ~ wait + travel + vcost, TravelMode, probit = TRUE)
## End(Not run)
## a mixed logit model
## Not run:
rpl <- mlogit(mode ~ price + catch | income, Fishing, varying = 2:9,
rpar = c(price= 'n', catch = 'n'), correlation = TRUE,
alton = NA, R = 50)
summary(rpl)
rpar(rpl)
cor.mlogit(rpl)
cov.mlogit(rpl)
rpar(rpl, "catch")
summary(rpar(rpl, "catch"))
## End(Not run)
# a ranked ordered model
data("Game", package = "mlogit")
g <- mlogit(ch ~ own | hours, Game, varying = 1:12, ranked = TRUE,
reflevel = "PC", idnames = c("chid", "alt"))
Example output
Loading required package: dfidx
Attaching package: ‘dfidx’
The following object is masked from ‘package:stats’:
filter
Call:
mlogit(formula = mode ~ price + catch, data = Fish, method = "nr")
Frequencies of alternatives:choice
beach boat charter pier
0.11337 0.35364 0.38240 0.15059
nr method
7 iterations, 0h:0m:0s
g'(-H)^-1g = 6.22E-06
successive function values within tolerance limits
Coefficients :
Estimate Std. Error z-value Pr(>|z|)
(Intercept):boat 0.8713749 0.1140428 7.6408 2.154e-14 ***
(Intercept):charter 1.4988884 0.1329328 11.2755 < 2.2e-16 ***
(Intercept):pier 0.3070552 0.1145738 2.6800 0.0073627 **
price -0.0247896 0.0017044 -14.5444 < 2.2e-16 ***
catch 0.3771689 0.1099707 3.4297 0.0006042 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Log-Likelihood: -1230.8
McFadden R^2: 0.17823
Likelihood ratio test : chisq = 533.88 (p.value = < 2.22e-16)
Call:
mlogit(formula = mode ~ 0 | income, data = Fish, method = "nr")
Frequencies of alternatives:choice
beach boat charter pier
0.11337 0.35364 0.38240 0.15059
nr method
4 iterations, 0h:0m:0s
g'(-H)^-1g = 8.32E-07
gradient close to zero
Coefficients :
Estimate Std. Error z-value Pr(>|z|)
(Intercept):boat 7.3892e-01 1.9673e-01 3.7560 0.0001727 ***
(Intercept):charter 1.3413e+00 1.9452e-01 6.8955 5.367e-12 ***
(Intercept):pier 8.1415e-01 2.2863e-01 3.5610 0.0003695 ***
income:boat 9.1906e-05 4.0664e-05 2.2602 0.0238116 *
income:charter -3.1640e-05 4.1846e-05 -0.7561 0.4495908
income:pier -1.4340e-04 5.3288e-05 -2.6911 0.0071223 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Log-Likelihood: -1477.2
McFadden R^2: 0.013736
Likelihood ratio test : chisq = 41.145 (p.value = 6.0931e-09)
# weights: 12 (6 variable)
initial value 1638.599935
iter 10 value 1477.150646
final value 1477.150569
converged
Call:
nnet::multinom(formula = mode ~ income, data = Fishing)
Coefficients:
(Intercept) income
pier 0.8141506 -1.434028e-04
boat 0.7389178 9.190824e-05
charter 1.3412901 -3.163844e-05
Std. Errors:
(Intercept) income
pier 5.816490e-09 2.668383e-05
boat 3.209473e-09 2.057825e-05
charter 3.921689e-09 2.116425e-05
Residual Deviance: 2954.301
AIC: 2966.301
Call:
mlogit(formula = mode ~ price + catch | income, data = Fish,
method = "nr")
Frequencies of alternatives:choice
beach boat charter pier
0.11337 0.35364 0.38240 0.15059
nr method
7 iterations, 0h:0m:0s
g'(-H)^-1g = 1.37E-05
successive function values within tolerance limits
Coefficients :
Estimate Std. Error z-value Pr(>|z|)
(Intercept):boat 5.2728e-01 2.2279e-01 2.3667 0.0179485 *
(Intercept):charter 1.6944e+00 2.2405e-01 7.5624 3.952e-14 ***
(Intercept):pier 7.7796e-01 2.2049e-01 3.5283 0.0004183 ***
price -2.5117e-02 1.7317e-03 -14.5042 < 2.2e-16 ***
catch 3.5778e-01 1.0977e-01 3.2593 0.0011170 **
income:boat 8.9440e-05 5.0067e-05 1.7864 0.0740345 .
income:charter -3.3292e-05 5.0341e-05 -0.6613 0.5084031
income:pier -1.2758e-04 5.0640e-05 -2.5193 0.0117582 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Log-Likelihood: -1215.1
McFadden R^2: 0.18868
Likelihood ratio test : chisq = 565.17 (p.value = < 2.22e-16)
Call:
mlogit(formula = mode ~ price + catch | income, data = Fishing2, shape = "wide", varying = 2:9, method = "nr")
Coefficients:
(Intercept):boat (Intercept):charter (Intercept):pier
5.2790e-01 1.6948e+00 7.7663e-01
price catch income:boat
-2.5110e-02 3.5768e-01 8.9122e-05
income:charter income:pier
-3.3611e-05 -1.2700e-04
Call:
mlogit(formula = choice ~ wait + gcost | income + size, data = Tr2, method = "nr")
Coefficients:
(Intercept):train (Intercept):bus (Intercept):car wait
-2.3115942 -3.4504941 -7.8913907 -0.1013180
gcost income:train income:bus income:car
-0.0197064 -0.0589804 -0.0277037 -0.0041153
size:train size:bus size:car
1.3289497 1.0090796 1.0392585
Call:
mlogit(formula = mode ~ price + catch | income, data = Fishing,
rpar = c(price = "n", catch = "n"), R = 50, correlation = TRUE,
varying = 2:9, alton = NA)
Frequencies of alternatives:choice
beach boat charter pier
0.11337 0.35364 0.38240 0.15059
bfgs method
17 iterations, 0h:0m:9s
g'(-H)^-1g = 1.3E-07
gradient close to zero
Coefficients :
Estimate Std. Error z-value Pr(>|z|)
(Intercept):boat 3.4903e-01 2.6558e-01 1.3142 0.1887779
(Intercept):charter 2.1865e+00 3.0504e-01 7.1680 7.612e-13 ***
(Intercept):pier 7.4647e-01 2.1246e-01 3.5135 0.0004422 ***
price -4.4544e-02 4.9868e-03 -8.9325 < 2.2e-16 ***
catch 2.8054e-01 1.5687e-01 1.7884 0.0737120 .
income:boat 1.0513e-04 5.8634e-05 1.7929 0.0729872 .
income:charter -4.0786e-05 5.9634e-05 -0.6839 0.4940114
income:pier -1.2163e-04 4.7312e-05 -2.5708 0.0101451 *
chol.price:price 2.3047e-02 4.1211e-03 5.5925 2.238e-08 ***
chol.price:catch 7.5142e-01 3.6695e-01 2.0477 0.0405860 *
chol.catch:catch 1.3290e-02 7.8229e-01 0.0170 0.9864459
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Log-Likelihood: -1185.9
McFadden R^2: 0.20819
Likelihood ratio test : chisq = 623.63 (p.value = < 2.22e-16)
random coefficients
Min. 1st Qu. Median Mean 3rd Qu. Max.
price -Inf -0.06008954 -0.04454446 -0.04454446 -0.02899938 Inf
catch -Inf -0.22636264 0.28054193 0.28054193 0.78744649 Inf
$price
normal distribution with parameters -0.045 (mean) and 0.023 (sd)
$catch
normal distribution with parameters 0.281 (mean) and 0.752 (sd)
price catch
price 1.0000000 0.9998436
catch 0.9998436 1.0000000
price catch
price 0.0005311717 0.01731811
catch 0.0173181068 0.56480911
normal distribution with parameters 0.281 (mean) and 0.752 (sd)
Min. 1st Qu. Median Mean 3rd Qu. Max.
-Inf -0.2263626 0.2805419 0.2805419 0.7874465 Inf
mlogit documentation built on Oct. 23, 2020, 5:29 p.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
Estimation by maximum likelihood of the multinomial logit model, with alternative-specific and/or individual specific variables.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | mlogit(
formula,
data,
subset,
weights,
na.action,
start = NULL,
alt.subset = NULL,
reflevel = NULL,
nests = NULL,
un.nest.el = FALSE,
unscaled = FALSE,
heterosc = FALSE,
rpar = NULL,
probit = FALSE,
R = 40,
correlation = FALSE,
halton = NULL,
random.nb = NULL,
panel = FALSE,
estimate = TRUE,
seed = 10,
...
)
|
Arguments
formula |
a symbolic description of the model to be estimated, |
data |
the data: an |
subset |
an optional vector specifying a subset of
observations for |
weights |
an optional vector of weights, |
na.action |
a function which indicates what should happen when
the data contains |
start |
a vector of starting values, |
alt.subset |
a vector of character strings containing the subset of alternative on which the model should be estimated, |
reflevel |
the base alternative (the one for which the coefficients of individual-specific variables are normalized to 0), |
nests |
a named list of characters vectors, each names being a nest, the corresponding vector being the set of alternatives that belong to this nest, |
un.nest.el |
a boolean, if |
unscaled |
a boolean, if |
heterosc |
a boolean, if |
rpar |
a named vector whose names are the random parameters
and values the distribution : |
probit |
if |
R |
the number of function evaluation for the gaussian
quadrature method used if |
correlation |
only relevant if |
halton |
only relevant if |
random.nb |
only relevant if |
panel |
only relevant if |
estimate |
a boolean indicating whether the model should be
estimated or not: if not, the |
seed |
the seed to use for random numbers (for mixed logit and probit models), |
... |
further arguments passed to |
Details
For how to use the formula argument, see Formula().
The data argument may be an ordinary data.frame. In this case,
some supplementary arguments should be provided and are passed to
mlogit.data(). Note that it is not necessary to indicate the
choice argument as it is deduced from the formula.
The model is estimated using the mlogit.optim().
function.
The basic multinomial logit model and three important extentions of this model may be estimated.
If heterosc=TRUE, the heteroscedastic logit model is estimated.
J - 1 extra coefficients are estimated that represent the scale
parameter for J - 1 alternatives, the scale parameter for the
reference alternative being normalized to 1. The probabilities
don't have a closed form, they are estimated using a gaussian
quadrature method.
If nests is not NULL, the nested logit model is estimated.
If rpar is not NULL, the random parameter model is estimated.
The probabilities are approximated using simulations with R draws
and halton sequences are used if halton is not
NULL. Pseudo-random numbers are drawns from a standard normal and
the relevant transformations are performed to obtain numbers drawns
from a normal, log-normal, censored-normal or uniform
distribution. If correlation = TRUE, the correlation between the
random parameters are taken into account by estimating the
components of the cholesky decomposition of the covariance
matrix. With G random parameters, without correlation G standard
deviations are estimated, with correlation G * (G + 1) /2
coefficients are estimated.
Value
An object of class "mlogit", a list with elements:
coefficients: the named vector of coefficients,
logLik: the value of the log-likelihood,
hessian: the hessian of the log-likelihood at convergence,
gradient: the gradient of the log-likelihood at convergence,
call: the matched call,
est.stat: some information about the estimation (time used, optimisation method),
freq: the frequency of choice,
residuals: the residuals,
fitted.values: the fitted values,
formula: the formula (a
Formulaobject),expanded.formula: the formula (a
formulaobject),model: the model frame used,
index: the index of the choice and of the alternatives.
Author(s)
Yves Croissant
References
\insertRefMCFA:73mlogit
\insertRefMCFA:74mlogit
\insertRefTRAI:09mlogit
See Also
mlogit.data() to shape the data. nnet::multinom() from
package nnet performs the estimation of the multinomial logit
model with individual specific variables. mlogit.optim()
details about the optimization function.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 | ## Cameron and Trivedi's Microeconometrics p.493 There are two
## alternative specific variables : price and catch one individual
## specific variable (income) and four fishing mode : beach, pier, boat,
## charter
data("Fishing", package = "mlogit")
Fish <- dfidx(Fishing, varying = 2:9, shape = "wide", choice = "mode")
## a pure "conditional" model
summary(mlogit(mode ~ price + catch, data = Fish))
## a pure "multinomial model"
summary(mlogit(mode ~ 0 | income, data = Fish))
## which can also be estimated using multinom (package nnet)
summary(nnet::multinom(mode ~ income, data = Fishing))
## a "mixed" model
m <- mlogit(mode ~ price + catch | income, data = Fish)
summary(m)
## same model with charter as the reference level
m <- mlogit(mode ~ price + catch | income, data = Fish, reflevel = "charter")
## same model with a subset of alternatives : charter, pier, beach
m <- mlogit(mode ~ price + catch | income, data = Fish,
alt.subset = c("charter", "pier", "beach"))
## model on unbalanced data i.e. for some observations, some
## alternatives are missing
# a data.frame in wide format with two missing prices
Fishing2 <- Fishing
Fishing2[1, "price.pier"] <- Fishing2[3, "price.beach"] <- NA
mlogit(mode ~ price + catch | income, Fishing2, shape = "wide", varying = 2:9)
# a data.frame in long format with three missing lines
data("TravelMode", package = "AER")
Tr2 <- TravelMode[-c(2, 7, 9),]
mlogit(choice ~ wait + gcost | income + size, Tr2)
## An heteroscedastic logit model
data("TravelMode", package = "AER")
hl <- mlogit(choice ~ wait + travel + vcost, TravelMode, heterosc = TRUE)
## A nested logit model
TravelMode$avincome <- with(TravelMode, income * (mode == "air"))
TravelMode$time <- with(TravelMode, travel + wait)/60
TravelMode$timeair <- with(TravelMode, time * I(mode == "air"))
TravelMode$income <- with(TravelMode, income / 10)
# Hensher and Greene (2002), table 1 p.8-9 model 5
TravelMode$incomeother <- with(TravelMode, ifelse(mode %in% c('air', 'car'), income, 0))
nl <- mlogit(choice ~ gcost + wait + incomeother, TravelMode,
nests = list(public = c('train', 'bus'), other = c('car','air')))
# same with a comon nest elasticity (model 1)
nl2 <- update(nl, un.nest.el = TRUE)
## a probit model
## Not run:
pr <- mlogit(choice ~ wait + travel + vcost, TravelMode, probit = TRUE)
## End(Not run)
## a mixed logit model
## Not run:
rpl <- mlogit(mode ~ price + catch | income, Fishing, varying = 2:9,
rpar = c(price= 'n', catch = 'n'), correlation = TRUE,
alton = NA, R = 50)
summary(rpl)
rpar(rpl)
cor.mlogit(rpl)
cov.mlogit(rpl)
rpar(rpl, "catch")
summary(rpar(rpl, "catch"))
## End(Not run)
# a ranked ordered model
data("Game", package = "mlogit")
g <- mlogit(ch ~ own | hours, Game, varying = 1:12, ranked = TRUE,
reflevel = "PC", idnames = c("chid", "alt"))
|
Example output
Loading required package: dfidx
Attaching package: ‘dfidx’
The following object is masked from ‘package:stats’:
filter
Call:
mlogit(formula = mode ~ price + catch, data = Fish, method = "nr")
Frequencies of alternatives:choice
beach boat charter pier
0.11337 0.35364 0.38240 0.15059
nr method
7 iterations, 0h:0m:0s
g'(-H)^-1g = 6.22E-06
successive function values within tolerance limits
Coefficients :
Estimate Std. Error z-value Pr(>|z|)
(Intercept):boat 0.8713749 0.1140428 7.6408 2.154e-14 ***
(Intercept):charter 1.4988884 0.1329328 11.2755 < 2.2e-16 ***
(Intercept):pier 0.3070552 0.1145738 2.6800 0.0073627 **
price -0.0247896 0.0017044 -14.5444 < 2.2e-16 ***
catch 0.3771689 0.1099707 3.4297 0.0006042 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Log-Likelihood: -1230.8
McFadden R^2: 0.17823
Likelihood ratio test : chisq = 533.88 (p.value = < 2.22e-16)
Call:
mlogit(formula = mode ~ 0 | income, data = Fish, method = "nr")
Frequencies of alternatives:choice
beach boat charter pier
0.11337 0.35364 0.38240 0.15059
nr method
4 iterations, 0h:0m:0s
g'(-H)^-1g = 8.32E-07
gradient close to zero
Coefficients :
Estimate Std. Error z-value Pr(>|z|)
(Intercept):boat 7.3892e-01 1.9673e-01 3.7560 0.0001727 ***
(Intercept):charter 1.3413e+00 1.9452e-01 6.8955 5.367e-12 ***
(Intercept):pier 8.1415e-01 2.2863e-01 3.5610 0.0003695 ***
income:boat 9.1906e-05 4.0664e-05 2.2602 0.0238116 *
income:charter -3.1640e-05 4.1846e-05 -0.7561 0.4495908
income:pier -1.4340e-04 5.3288e-05 -2.6911 0.0071223 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Log-Likelihood: -1477.2
McFadden R^2: 0.013736
Likelihood ratio test : chisq = 41.145 (p.value = 6.0931e-09)
# weights: 12 (6 variable)
initial value 1638.599935
iter 10 value 1477.150646
final value 1477.150569
converged
Call:
nnet::multinom(formula = mode ~ income, data = Fishing)
Coefficients:
(Intercept) income
pier 0.8141506 -1.434028e-04
boat 0.7389178 9.190824e-05
charter 1.3412901 -3.163844e-05
Std. Errors:
(Intercept) income
pier 5.816490e-09 2.668383e-05
boat 3.209473e-09 2.057825e-05
charter 3.921689e-09 2.116425e-05
Residual Deviance: 2954.301
AIC: 2966.301
Call:
mlogit(formula = mode ~ price + catch | income, data = Fish,
method = "nr")
Frequencies of alternatives:choice
beach boat charter pier
0.11337 0.35364 0.38240 0.15059
nr method
7 iterations, 0h:0m:0s
g'(-H)^-1g = 1.37E-05
successive function values within tolerance limits
Coefficients :
Estimate Std. Error z-value Pr(>|z|)
(Intercept):boat 5.2728e-01 2.2279e-01 2.3667 0.0179485 *
(Intercept):charter 1.6944e+00 2.2405e-01 7.5624 3.952e-14 ***
(Intercept):pier 7.7796e-01 2.2049e-01 3.5283 0.0004183 ***
price -2.5117e-02 1.7317e-03 -14.5042 < 2.2e-16 ***
catch 3.5778e-01 1.0977e-01 3.2593 0.0011170 **
income:boat 8.9440e-05 5.0067e-05 1.7864 0.0740345 .
income:charter -3.3292e-05 5.0341e-05 -0.6613 0.5084031
income:pier -1.2758e-04 5.0640e-05 -2.5193 0.0117582 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Log-Likelihood: -1215.1
McFadden R^2: 0.18868
Likelihood ratio test : chisq = 565.17 (p.value = < 2.22e-16)
Call:
mlogit(formula = mode ~ price + catch | income, data = Fishing2, shape = "wide", varying = 2:9, method = "nr")
Coefficients:
(Intercept):boat (Intercept):charter (Intercept):pier
5.2790e-01 1.6948e+00 7.7663e-01
price catch income:boat
-2.5110e-02 3.5768e-01 8.9122e-05
income:charter income:pier
-3.3611e-05 -1.2700e-04
Call:
mlogit(formula = choice ~ wait + gcost | income + size, data = Tr2, method = "nr")
Coefficients:
(Intercept):train (Intercept):bus (Intercept):car wait
-2.3115942 -3.4504941 -7.8913907 -0.1013180
gcost income:train income:bus income:car
-0.0197064 -0.0589804 -0.0277037 -0.0041153
size:train size:bus size:car
1.3289497 1.0090796 1.0392585
Call:
mlogit(formula = mode ~ price + catch | income, data = Fishing,
rpar = c(price = "n", catch = "n"), R = 50, correlation = TRUE,
varying = 2:9, alton = NA)
Frequencies of alternatives:choice
beach boat charter pier
0.11337 0.35364 0.38240 0.15059
bfgs method
17 iterations, 0h:0m:9s
g'(-H)^-1g = 1.3E-07
gradient close to zero
Coefficients :
Estimate Std. Error z-value Pr(>|z|)
(Intercept):boat 3.4903e-01 2.6558e-01 1.3142 0.1887779
(Intercept):charter 2.1865e+00 3.0504e-01 7.1680 7.612e-13 ***
(Intercept):pier 7.4647e-01 2.1246e-01 3.5135 0.0004422 ***
price -4.4544e-02 4.9868e-03 -8.9325 < 2.2e-16 ***
catch 2.8054e-01 1.5687e-01 1.7884 0.0737120 .
income:boat 1.0513e-04 5.8634e-05 1.7929 0.0729872 .
income:charter -4.0786e-05 5.9634e-05 -0.6839 0.4940114
income:pier -1.2163e-04 4.7312e-05 -2.5708 0.0101451 *
chol.price:price 2.3047e-02 4.1211e-03 5.5925 2.238e-08 ***
chol.price:catch 7.5142e-01 3.6695e-01 2.0477 0.0405860 *
chol.catch:catch 1.3290e-02 7.8229e-01 0.0170 0.9864459
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Log-Likelihood: -1185.9
McFadden R^2: 0.20819
Likelihood ratio test : chisq = 623.63 (p.value = < 2.22e-16)
random coefficients
Min. 1st Qu. Median Mean 3rd Qu. Max.
price -Inf -0.06008954 -0.04454446 -0.04454446 -0.02899938 Inf
catch -Inf -0.22636264 0.28054193 0.28054193 0.78744649 Inf
$price
normal distribution with parameters -0.045 (mean) and 0.023 (sd)
$catch
normal distribution with parameters 0.281 (mean) and 0.752 (sd)
price catch
price 1.0000000 0.9998436
catch 0.9998436 1.0000000
price catch
price 0.0005311717 0.01731811
catch 0.0173181068 0.56480911
normal distribution with parameters 0.281 (mean) and 0.752 (sd)
Min. 1st Qu. Median Mean 3rd Qu. Max.
-Inf -0.2263626 0.2805419 0.2805419 0.7874465 Inf
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